Hierarchically specified unit disk graphs

Theoretical Computer Science

Volumn 174, Issue 1-2, 1997, Pages 23-65

  Marathe, Madhav V ^a   Radhakrishnan, Venkatesh ^b   Hunt III, Harry B ^c   Ravi, S S ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b HEWLETT PACKARD COMPANY   (United States)

^c STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

HIERARCHICAL SPECIFICATIONS; UNIT DISK GRAPHS;

GRAPH THEORY;

EID: 0346675349     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(96)00008-4     Document Type: Article

References (38)

1. S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy, Proof verification and hardness of approximation problems, in: Proc. 33rd Annual IEEE Conf. on Foundations of Computer Science (FOCS) (1992) 14-23.
2. J.L. Bentley, T. Ottmann and P. Widmayer, The complexity of manipulating hierarchically defined set of rectangles, in: F.P. Preparata, ed:, Advances in Computing Research, Vol. 1 (Jai press inc, Greenwich, Ct, 1984) 127-158.
3. B.N. Clark, C.J. Colbourn and D.S. Johnson, Unit disk graphs, Discrete Math. 86 (1990) 165-177.
4. E. Cohen and N. Megiddo, Strongly polynomial-time and NC algorithms for detecting cycles in dynamic graphs, in: Proc. 21st Annual ACM Symp. on Theory of Computing (STOC) (1989) 523-534.
5. A. Condon, J. Feigenbaum, C. Lund and P. Shor, Probabilistically checkable debate systems and approximation algorithms for PSPACE-Hard Functions, Proc. 25th Annual ACM Symp. on Theory of Computing (STOC) (1993) 305-313.
6. A. Condon, J. Feigenbaum, C. Lund and P. Shor, Random debators and the hardness of approximating stochastic functions for PSPACE-hard functions, Proc. 9th ACM Annual Conf. on Structure in Complexity Theory (1994) 280-293.
7. R.J. Fowler, M.S. Paterson and S.L. Tanimoto, Optimal packing and covering in the plane are NP-complete, Inform. Process. Lett. 12 (3) (1981) 133-137.
8. H. Galperin, Succinct representation of graphs, Ph.D. Thesis, Princeton University, 1982.
9. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, CA, 1979).
10. C. Ghezzi, M. Jazayeri and D. Mandrioli, Fundamentals of Software Engineering (Prentice Hall, Englewood Cliffs, NJ, 1991).
11. M. Halldórsson, Approximating discrete collections via local improvements, Proc. 6th ACM-SIAM Symp. on Discrete Algorithms (SODA) (1995) 160-169.
12. D.S. Hochbaum and W. Maass, Approximation schemes for covering and packing problems in image processing and VLSI, J. ACM 32 (1) (1985) 130-136.
13. F. Höfting, T. Lengauer and E. Wanke, Processing of hierarchically defined graphs and graph families, in: Data Structures and Efficient Algorithms (Final Report on the DFG Special Joint Initiative), Lecture Notes in Computer Science, Vol. 594 (Springer, New York, 1992) 44-69.
14. F. Höfting and E. Wanke, Minimum cost paths in periodic graphs, Tech. Report 99, Universit ät-Gesamthochschule-Paderborn, FRG, April, 1992 . An extended abstract of this paper appears in Proc. 4th ACM-SIAM Symp. on Discrete Algorithms (SODA) (1993) 493-499.
15. F. Höfting and E. Wanke, Minimum cost paths in periodic graphs, Tech. Report 99, Universit ät- Gesamthochschule-Paderborn, FRG, April, 1992 . An extended abstract of this paper appears in Proc. 4th ACM-SIAM Symp. on Discrete Algorithms (SODA) (1993) 493-499.
16. H.B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz and R.E. Stearns, A unified approach to approximation schemes for NP- and PSPACE-hard problems for geometric graphs, Proc. 2nd Annual European Symp. on Algorithms (ESA) (1994) 424-435.
17. T. Lengauer, Exploiting hierarchy in VLSI design, Proc. AWOC'86, Lecture Notes in Computer Science, Vol. 227 (Springer, New York, 1986) 180-193.
18. T. Lengauer, Efficient algorithms for finding minimum spanning forests of hierarchically defined graphs, J. Algorithms 8 (1987) 260-284.
19. T. Lengauer, Hierarchical planarity testing, J. ACM 36 (3) (1989) 474-509.
20. T. Lengauer and K.W. Wagner, The correlation between the complexities of non-hierarchical and hierarchical versions of graph problems, J. Comput. System Sci. 44 (1992) 63-93.
21. T. Lengauer and E. Wanke, Efficient solutions for connectivity problems for hierarchically defined graphs, SIAM J. Comput. 17 (6) (1988) 1063-1080.
22. T. Lengauer and C. Wieners, Efficient solutions for hierarchical systems of linear equations, Computing 39 (1987) 111-132.
23. C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, in: Proc. 25th Annual ACM Symp. on Theory of Computing (STOC) (1993) 286-293. (A complete version of this paper appears in J. ACM 41 (5) (1994) 960-981.)
24. C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, in: Proc. 25th Annual ACM Symp. on Theory of Computing (STOC) (1993) 286-293. (A complete version of this paper appears in J. ACM 41 (5) (1994) 960-981.)
25. M.V. Marathe, H. Breu, H.B. Hunt III, S.S. Ravi and D.J. Rosenkrantz, Simple heuristics for unit disk graphs, Networks 25 (2) (1995) 59-68.
26. M.V. Marathe, H.B. Hunt III and S.S. Ravi, The complexity of approximating PSPACE-complete problems for hierarchical specifications, Proc. 20th International Colloquium on Automata, Languages and Programming (ICALP) (1993) 76-87. (A Complete version of this paper appears in Nordic J. Comput. 1 (1994) 275-316.)
27. M.V. Marathe, H.B. Hunt III and S.S. Ravi, The complexity of approximating PSPACE-complete problems for hierarchical specifications, Proc. 20th International Colloquium on Automata, Languages and Programming (ICALP) (1993) 76-87. (A Complete version of this paper appears in Nordic J. Comput. 1 (1994) 275-316.)
28. M.V. Marathe, H.B. Hunt III, R.E. Stearns and V. Radhakrishnan, Approximation schemes for PSPACE-complete problems for succinct graphs, Proc. 26th Annual ACM Symp. on the Theory of Computing (STOC) (1994) 468-477.
29. M.V. Marathe, H.B. Hunt III, R.E. Stearns and V. Radhakrishnan, Complexity of hierarchically and 1-dimensional periodically specified problems, Technical Report No. LA-UR-95-3348, Los Alamos National Laboratory, 1995.
30. M.V. Marathe, H.B. Hunt III and R.E. Stearns, Complexity of succinctly presented geometric graph problems, Manuscript, 1995.
31. J.O. McClain, L.J. Thomas and J.B. Mazzola, Operations Management (Prentice-Hall, Englewood Cliffs, NJ, 1992).
32. C. Mead and L. Conway, Introduction to VLSI systems (Addison-Wesley, Reading, MA, 1980).
33. N. Meggido and K. Supowit, On the complexity of some common geometric location problems, SIAM J. Comput. 13 (1) (1984) 182-196.
34. J.B. Orlin, Some problems on dynamic/periodic graphs, in: Progress in Combinatorial Optimization (Academic Press, New York, 1984) 273-293.
35. J.D. Ullman, Principles of Database and Knowledge Base Systems, Vol. 1 (Computer Science Press. Rockville, MD, 1988).
36. K.W. Wagner, The complexity of problems concerning graphs with regularities, Proc. 11th Symp. on Math. Foundations of Computer Science (MFCS), Lecture Notes in Computer Science, Vol. 176 (Springer, New york, 1984) 544-552.
37. M. Williams, Efficient processing of hierarchical graphs, Technical Report 90-06, Dept. Computer Science, Iowa Sate University. (Parts of the report appeared in WADS'89 and SWAT'90 co-authored with D. Fernandez-Baca.)
38. D.W. Wang and Y.S. Kuo, A study on geometric location problems, Inform. Process. Lett. 28 (6) (1988) 281-286.